In a cyclic quadrilateral ABCD, the diagonal AC bisects the angle C. Which of the following statements is/are correct? I. ∠ABD = ∠ADB II. The diagonal BD is parallel to the tangent of the circle at A Select the answer using the code given below:

CDS 2026 PYQ with Answer — In a cyclic quadrilateral ABCD, the diagonal AC bisects the angle C.…

2026 · Q46

In a cyclic quadrilateral ABCD, the diagonal AC bisects the angle C. Which of the following statements is/are correct?

I∠ABD = ∠ADB
IIThe diagonal BD is parallel to the tangent of the circle at A Select the answer using the code given below:

Elementary MathematicsCircles

AI only
BII only
CBoth I and II
DNeither I nor II

Explanation

Since AC bisects ∠C, ∠BCA=∠ACD, so the arcs BA and AD (and chords BA, AD) are equal; then in ΔABD the base angles ∠ABD and ∠ADB are equal — I is correct. The tangent-chord angle between the tangent at A and AB equals ∠ACB (alternate segment), which subtends arc AB, the same arc ∠ABD subtends, so BD is parallel to the tangent — II is correct. Both are correct, option C.